There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π)
Area of a circle = πr2
0.02 bacteria per square millimeter
0.42 bacteria per square millimeter
2.39 bacteria per square millimeter
52.5 bacteria per square millimeter
The approximate Population density in the circular petri dish with a radius of 40 millimeters and 2,100 bacteria is approximately 0.418 bacteria per square millimeter. After rounding up the bacteria becomes 0.42 per sq. meter hence the correct option is b
The approximate population density in the circular petri dish, we need to calculate the area of the dish and divide the total number of bacteria by that area.
The formula to calculate the area of a circle is: A = πr^2, where A represents the area and r is the radius.
In this case, the radius of the petri dish is given as 40 millimeters. Therefore, the area can be calculated as follows:
A = 3.14 * (40)^2
A = 3.14 * 1600
A ≈ 5024 square millimeters
Next, we divide the total number of bacteria (2,100) by the calculated area to find the population density:
Population density = 2,100 bacteria / 5024 square millimeters
Population density ≈ 0.418 bacteria per square millimeter
Therefore, the approximate population density in the circular petri dish is 0.418 bacteria per square millimeter.
in scientific calculations, it is customary to use the value of π as 3.14 for simplicity, even though it is an irrational number with a longer decimal representation.
When writing about scientific concepts or calculations, it is crucial to ensure academic integrity by avoiding plagiarism. This can be done by understanding and explaining the concepts in your own words, citing any external sources used, and providing accurate calculations based on the given information.
In conclusion, the approximate population density in the circular petri dish with a radius of 40 millimeters and 2,100 bacteria is approximately 0.418 bacteria per square millimeter. After rounding up the bacteria becomes 0.42 per sq. meter hence the correct option is b
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Use Cramer's rule to solve the following equation systems A2 JA A VAL 8x1 + 9x2 + 413 = 2 11 +212 + 313 = 3 711 + 6x2 + 5/3 = 1 The solutions are x; = 4,15 = , and ; = What are All, a; and|A3/? 1. |4,1 = -60, x) = -1, and |A3= -60 2. [A1] = -78, 3) = -0.7, and |A3] = 28 3. |A1 = -60, ; = 1, and A3] = 36 4. |A 1 = -78, x = 1.25, and |A3| = 52 2. Given the function y = f(r) = 57- 4r. (a) Find the difference quotient as a function of and Ar. 1. 10.r - 4 2. 5.r? - 4r 3. 5(Ar)? - 4A: 4. 10.r + 5Ar - 4 (b) Find f'(-1) and f'(5). 1. S'(-1) = 9 and f'(5) = 105 2. f'(-1) = -14 and f'(5) = 46 3. $'(-1) = -14 and f'(5) = 105 4. f'(-1) = -19 and f'(5) = 71
1) The solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
2) The difference quotient as a function of Δr is -4.
3) f'(-1) = -4 and f'(5) = -4.
To solve the equation system using Cramer's rule, we need to find the determinant of the coefficient matrix A and the determinants of the matrices obtained by replacing each column of A with the column on the right-hand side.
The given equation system is:
8x₁ + 9x₂ = 2
11x₁ + 2x₂ = 3
7x₁ + 6x₂ = 1
Step 1: Calculate the determinant of the coefficient matrix A.
A = |8 9|
|11 2|
|7 6|
|A| = (8 * 2) - (9 * 11)
= -78
Step 2: Calculate the determinant of the matrix obtained by replacing the first column of A with the column on the right-hand side.
A₁ = |2 9|
|3 2|
|1 6|
|A₁| = (2 * 2) - (9 * 3)
= -22
Step 3: Calculate the determinant of the matrix obtained by replacing the second column of A with the column on the right-hand side.
A₂ = |8 2|
|11 3|
|7 1|
|A₂| = (8 * 3) - (2 * 11)
= 14
Step 4: Calculate the solutions x₁ and x₂ using Cramer's rule.
x₁ = |A₁| / |A|
= -22 / -78
= 11/39
x₂ = |A₂| / |A|
= 14 / -78
= -7/39
Therefore, the solutions to the equation system are x₁ = 11/39 and x₂ = -7/39.
Now, let's move on to the second part of your question regarding the function f(r) = 57 - 4r.
(a) To find the difference quotient as a function of Δr (Δr represents the change in r):
Difference quotient = (f(r + Δr) - f(r)) / Δr
Expanding and simplifying the expression:
Difference quotient = (57 - 4(r + Δr) - (57 - 4r)) / Δr
= (57 - 4r - 4Δr - 57 + 4r) / Δr
= -4Δr / Δr
= -4
Therefore, the difference quotient as a function of Δr is -4.
(b) To find f'(-1) and f'(5), we need to find the derivative of f(r) with respect to r.
f'(r) = d/dx (57 - 4r)
= -4
Substituting r = -1 and r = 5 into f'(r), we get:
f'(-1) = -4
f'(5) = -4
Therefore, f'(-1) = -4 and f'(5) = -4.
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A helicopter hovers 1150 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 39° How far off the coast to the nearest foot is island?
i need the prosces plis is for tomorrow
Answer:
p) = 17/30 or 0.56
q) = 191/60 or 3 11/60
At a candy store, Layla bought 2 pounds of jelly beans and 4 pounds of gummy worms for $46. Meanwhile, Brittany bought 3 pounds of jelly beans and 2 pounds of gummy worms for $41. How much does the candy cost?
X= Y=
Answer:
X = $9.00 for 1 pound of Jelly Beans
Y = $7.00 for 1 pound of Gummy Worms
Step-by-step explanation:
Ok, to start we need to make up some notation. It looks like you've chosen X and Y as your variables which works for me.
First lets say X = cost of one pound of jelly beans and Y = cost of one pound of gummy worms
Now let's put together our equations
2X + 4Y = 46
3X + 2Y = 41
Now we need to solve for one of the variables using substitution or elimination. Since none of the variables are isolated, let's use elimination by multiplying the bottom equation by -2.
2X + 4Y = 46
-6X - 4Y = -82
___________
-4X + 0 = -36
-4X = -36
X = 9 or $9.00 per pound
Now we can plug that back into own of the equations and solve for Y
2(9) + 4Y = 46
18 + 4Y = 46
4Y = 28
Y = 7 or $7.00 per pound
Liz flips a coin 80 times. The coin lands heads up 32 times and tails up 48 times. Complete each statement. The theoretical probability of the coin landing heads up is 50%. (Type an integer or a decimal.) Based on Liz's results, the experimental probability of the coin landing heads up is
Answer:
40%
Step-by-step explanation:
Answer: 50, 60, Less.
Step-by-step explanation: The theoretical probability of the coin landing heads up is 50%
Based on Liz's results, the experimental probability of the coin landing heads up is 60
The theoretical probability is less than the experimental probability in this experiment.
Hope this helped have a nice day!
If a dog can eat 16 treats in 2 hours, how many can it eat in 6 hours?
Answer:
48 treats
Step-by-step explanation:
16 treats / 2 hours = 8 treats / hour
8 treats / hour x 6 hours =
48 treats
Hope that helps! :)
Assuming an individual has X hours per week during the summer to devote to taking classes or working for an employer. Also, assume that to receive at least a B or better, you must devote at least X hours per course per week (1 course = X hours per week, 2 courses = X hours per week, etc...) Explain why one faces a tradeoff between the number of courses and hours of work. Why would it be impossible to take X courses while working X hours per week? Why would taking one class and working X hours per week would result in large amount of free time?
One faces a tradeoff between the number of courses and hours of work due to limited available time. Taking X courses while working X hours per week is impossible as it exceeds the time constraint.
The tradeoff between the number of courses and hours of work arises due to the finite number of hours available in a week. Assuming an individual has X hours per week, this time must be divided between courses and work.
To achieve a B or better in a course, it is necessary to dedicate at least X hours per course per week. Therefore, taking X courses while working X hours per week would require dedicating X hours per course, resulting in a total time commitment exceeding the available X hours.
Conversely, if only one class is taken while working X hours per week, the time commitment for a single course is less than X hours. This scenario leaves a significant amount of free time remaining, as the total time dedicated to the course and work does not exhaust the available X hours.
In summary, the tradeoff occurs because the time available is limited, and the minimum time requirement per course restricts the number of courses that can be taken while maintaining a specific work schedule.
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Yasmin ordered 20 sandwiches for the STEM club's after school meeting. Some were turkey and some were ham sandwiches. Turkey sandwiches cost $5.50 and ham costs $4.50. The total bill was $97. How many turkey sandwiches were ordered?
7 TURKEY AND 13 HAM
I USED CALCULATOR BTW
Patrick left an $7 tip on a $53 restaurant bill. What percent tip is that?
The percent tip is 13.2%.
To find out what percentage Patrick gave as tip, we need to divide the tip amount by the total bill amount and then convert the result into a percentage.
For this question:
Patrick left an $7 tip on a $53 restaurant bill. What percent tip is that?
Solution:The percentage of tip can be found using the following formula:
% = (Tip amount / Total bill amount) x 100
Plugging in the given values we get:
% = (7 / 53) x 100% = 0.132 x 100% = 13.2 %
Therefore, Patrick gave a 13.2% tip on his restaurant bill.
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What is the area of a parallelogram that has a base of 4 ½ inc. and a height of 2 ¼ in. ?
Answer:
4.5
Step-by-step explanation:
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), E(2,2)2
,2
)), and F(32,−4232
,−42
), find the position vector equal to the following vectors.
AB⃗
AB
This indicates that vector 2AB has a length of 165.
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), and E, let's determine the length of the vector 2AB. To begin, we must determine the distance that separates points A and B. The distance formula is as follows: Equation for distance: We can calculate d as [(x2 - x1)2 + (y2 - y1)2] using the distance formula: Spot = [(6 - (- 2))2 + (16 - 0)2] = [(6 + 2)2 + (16)2] = [(8)2 + (16)2] = [(64 + 256) = 320 = 8] Now, we can deduct the directions of point A from guide B toward decide the vector Stomach muscle:
To find 2AB, simply multiply each part of AB by 2: AB = (6 - (-2)i + (16 - 0)j = 8i + 16j 2AB = 2(8i + 16j) = 16i + 32j. Last but not least, we must ascertain the magnitude of 2AB. The extent recipe is as per the following: Size formula: Using the magnitude formula, we get: ||v|| = (v12 + v22). ||2AB|| = (162 + 322) = (256 + 1024) = (1280 + 165). This indicates that vector 2AB has a length of 165.
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A sofa is 7 feet 5 inches long. How many inches is the sofa?
89 inches!
Because each foot is 12 inches and 12*7=84 and 84+5=89!
The stock of Company A gained 6% today to $94.87. What was the opening price of the stock in the beginning of the day?
Answer:
Step-by-step explanation:
I don’t know
We want to find the opening price of the stock in the beginning of the day. We will find that the solution is $89.50.
Working with percentages.
Let's say that the opening price of the stock was X.
Then, it is increased 6% to get to $94.87
This means that the 106% of X is equal to $94.87, then we can solve:
1.06*X = $94.87
Where we wrote 106% in decimal form, now we can just solve this for X:
X = $94.87/1.06 = $89.50
This means that the price of the stock in the beginning of the day was $89.50
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Michael's dog stands 10 feet from a table, and notices a plate resting on the edge of the table. The height from the ground to the top of the table is 4 feet, and his dog's eyes are 1 foot above the ground. What is the angle of elevation from Michael's dog to the plate? Round your answer to the nearest whole degree.
Answer:
The angle of elevation is 17°.
Step-by-step explanation:
Let's draw the scenario to better understand the problem:
Focusing on the right triangle formed, it appears that we get measures of the two sides of the right triangles.
Opposite Side = 3 Ft.
Adjacent Side = 10 Ft.
To find the angle of elevation, we will be using the Targent Function:
[tex]targent \: 0 = \frac{opposite \: side}{adjacent \: side} \\ targent \: 0 = \frac{3}{10} \\ 0 = {targent}^{ - 1} ( \frac{3}{10} ) \\ 0 = 16.69924423399 = 17[/tex]
Therefore, the angle of elevation is 17°.
BRAINLY TO WHOEVER HELPS AND GETS IT RIGHT
~no links pls~
Answer: A
Step-by-step explanation:
Similar Polygons
DEFG is similar to HJKL. What is the length of LK?
A) 5
B)21
C) 80/3
D) 60
Answer:
I think it's 21. .........
A wheel of the given radius is rotating at the indicated rate. radius 9 in., 2100 rpm (a) Find the angular speed (in radians per minute). radians per minute (b) Find the linear speed of a point on the circumference (in ft/min). (Round your answer to the nearest whole number.) ft/min
The linear speed of a point on the circumference is approximately 9895 feet per minute.
(a) To find the angular speed in radians per minute, we need to convert the given rotational speed from rpm (revolutions per minute) to radians per minute. Since there are 2π radians in one revolution, we can use the conversion factor:
Angular speed (in radians per minute) = Rotational speed (in rpm) * 2π
Given that the rotational speed is 2100 rpm, we can calculate the angular speed:
Angular speed = 2100 rpm * 2π ≈ 13194 radians per minute
Therefore, the angular speed of the wheel is approximately 13194 radians per minute.
(b) To find the linear speed of a point on the circumference in feet per minute, we can use the formula:
Linear speed = Angular speed * Radius
Given that the radius of the wheel is 9 inches, we need to convert it to feet:
Radius = 9 inches * (1 foot / 12 inches) = 0.75 feet
Now, we can calculate the linear speed:
Linear speed = 13194 radians per minute * 0.75 feet ≈ 9895 feet per minute
Therefore, the linear speed of a point on the circumference is approximately 9895 feet per minute.
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Use induction to prove that if A1, A2,...,An and B are sets,
then (A1 −B) ∩(A2 −B) ∩...∩(An−B) = (A1 ∩A2 ∩...∩An) −B.
It is proved that if A1, A2,...,An and B are sets, then (A1 −B) ∩(A2 −B) ∩...∩(An−B) = (A1 ∩A2 ∩...∩An) −B.
To prove the given statement using induction, we need to show that it holds true for a base case and then demonstrate that if it holds for an arbitrary value of 'n', it also holds for 'n + 1'.
Base Case (n = 1):
Let's consider the base case where 'n = 1'. We have two sets A1 and B, and we want to prove that (A1 - B) = (A1 - B).
(A1 - B) ∩ (A1 - B) = (A1 - B) [Using the definition of set difference]
This satisfies the given statement for the base case.
Inductive Step
Assuming that the given statement holds for 'n = k', let's prove that it holds for 'n = k + 1'.
We have sets A1, A2, ..., Ak+1, and B. We want to prove that:
(A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B) = (A1 ∩ A2 ∩ ... ∩ Ak+1) - B
Using the inductive hypothesis, we can rewrite the left-hand side (LHS) as:
[(A1 ∩ A2 ∩ ... ∩ Ak) - B] ∩ (Ak+1 - B)
To prove the equality, we need to show that each side is a subset of the other.
1. LHS ⊆ RHS:
Let x be an arbitrary element in LHS. This means that x belongs to each set in the intersection on the LHS: (A1 - B), (A2 - B), ..., (Ak+1 - B). By the definition of set intersection, x also belongs to (A1 - B), (A2 - B), ..., (Ak - B), and (Ak+1 - B).
Since x belongs to each set in the intersection (A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B), it follows that x belongs to (A1 ∩ A2 ∩ ... ∩ Ak) - B. Therefore, x ∈ RHS.
2. RHS ⊆ LHS:
Now let y be an arbitrary element in RHS. This means that y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1) - B. By the definition of set difference, y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1) and y does not belong to B.
Since y belongs to (A1 ∩ A2 ∩ ... ∩ Ak+1), it implies that y belongs to each set A1, A2, ..., Ak+1. By the definition of set difference, y does not belong to B, so y also belongs to each set (A1 - B), (A2 - B), ..., (Ak+1 - B).
Therefore, y ∈ LHS.
Since we have shown that LHS ⊆ RHS and RHS ⊆ LHS, it follows that (A1 - B) ∩ (A2 - B) ∩ ... ∩ (Ak+1 - B) = (A1 ∩ A2 ∩ ... ∩ Ak+1) - B.
By the principle of mathematical induction, the statement holds for all 'n', completing the proof.
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A rectangle with area 36 square inches has a length that is 3 less than 3 times the width. Find the length and the width of the rectangle.
Answer:
length = 9 in ; width = 4 in
Step-by-step explanation:
1) formula of the area of a rectangle
A = base x width
2) write an equation with the given informations:
w x (3w-3) = 36
3) solve the equation
- multiply W by 3w and -3
3w^2 -3w = 36
- divide the two members by 3
w^2 - w = 12
- add up -12 at the two members
w^2-w -12 = 12 -12
w^2 - w - 12 = 0
- find two numbers whose sum is -1 and whose product is -12 and factorise the equation
(w-4)(w+3) = 0
- find the two solutions
w-4 = 0
w = 4
w+3 = 0
w = -3
4)remember that a length can’t be negative.
w = 4 is the only solution
5) find the length
4x3 - 3 = 9
If the population density for the city is 10,000 people per square mile, what is the population of the city?
Answer:
10,000 * (square miles in the city)
Step-by-step explanation:
You've been given a population of people for every square mile (10,000) and you're trying to figure out how many people live in the city.
To convert people per a square mile into people, you'll need to know how many square miles you have. I assume you've been given this as the size of the city or how many square miles the city takes up. Just multiply the amount of people per a square mile by the amount of square miles in the city, and it'll give you the population of people in every square mile of the city (the population).
Note:
This is people per a square mile, or in other words, for every square mile of city, 10,000 people live there. If you have 2 square miles of city, then 2 * 10,000 = 20,000 people live there.
Eduardo bought 2-liter sports drink for soccer practice.During practice,Eduardo drank 250 millimeters of the sports drink.Then he drank another 1/2 liter of the drink after practice.How many milliters of the sports drink did Eduardo have left
Answer:
1,250 millileters
Step-by-step explanation:
The computation of the number of milliters of the sports drink left is shown below:
Given that
The 2-liter sports drink is purchased
And, drank 250 millimeters and than drank one-half liter of the drink
Now convert liter to millileter
1 litre = 1000 milliliter.
2 liters = 2 × 1000 milliliters.
= 2000 milliliters.
Now the left drink would be
= (2000 - 250) - (250 × 2)
= 1,750 - 500
= 1,250 millileters
trigonometry question
Answer:
Step-by-step explanation:
x = 87.2ft
Hope that helps :)
Item 7
A flat rate shipping box is in the shape of a rectangular prism. You estimate that the volume of the box is 350 cubic inches. You measure the box and find that it has a length of 10 inches, a width of 9 inches, and a height of 4.5 inches. Find the percent error. Round your answer to the nearest tenth of a percent.
Answer: the answer is 6.06%, however if it is rounded it's 6.0%
Step-by-step explanation:
Given the functions f(n)=11 and g(n)=((3)/(4))^(n-1), combine them to create a geometric sequence, a_(n), and solve for the 9 th term.
The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).
The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.
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a restaurant used 6.5 ounces of cheese to make 5 slices of pizza. if each slice had the same amount of cheese, how much was on each slice?
Answer:
1.3 ounces, 1.3*5 =6.5
Observa el siguiente polígono y responde la pregunta.
¿Cuál es el perímetro del polígono?
A.
13mn3+4m2+3mn2+2mn
B.
53mn3+4m2+2mn2+2mn
C.
13mn3+3m2+4mn2+3mn
D.
53mn3+3m2+2mn2+3mn
The correct option regarding the perimeter of the polygon in this problem is given as follows:
5/3mn³ + 3mn² + 3m².
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
Hence the expression for the perimeter is given as follows:
1/3mn³ + mn² + m² + 2mn³ + 2mn² + 3m².
Combining the like terms, the perimeter is given as follows:
5/3mn³ + 3mn² + 3m².
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PLEASE HELP!! I'll make brainliest
pleaseeeeeeeeeeee heeellllpppppppp i’ll mark u
Answer:
Add up all of the numbers, and divide by the number of digits. To put it another way, the total is divided by the count.
Step-by-step explanation:
so ... 2,4,4,2
2+4+4+2= 12
12 divided by 4=3
i think 3 is the mean....
hope this helps.....
1. The two sample t-test The carapace lengths (measure in mm) of crawfish (Palinurus vulgaris) captured in streams in Devon and Cornwall were measured. The data is given below: Carapace Length (in mm) Devon: 170,111,135,182,121,174,169,133,141,147,159,163 Cornwall: 146, 97, 102, 181, 107, 118,131,155,127,130, 129 a. Do you have reason to believe the two populations of crawfish do both have the same mean carapace length? Use the t test. b. Can you answer the question in a. using the Wilcoxon rank sum test? (See note below.) c. Compare the results obtained in a. and b. Are you surprised? The Wilcoxon Rank Sum Test - The Wilcoxon Rank Sum (WRS) test is the distribution free alternative to the t-test. It does not consider the actual value of the observations but only their relative position in the combined set of observations from the two samples, A and B. To use the WRS, you combine the observations of the two samples, order them from smallest to the largest, given rank 1 to the smallest observation (in either sample), rank 2 to the second smallest, and so on, giving rank n+m to the largest observation. The null hypothesis is that the two distributions are the same. The test statistic, WA or WB is the sum of the ranks of the observations in one of the samples. Reference Distribution For samples of similar sized with a combined number of observation in excess of 20, if H0 is true WA will have a distribution that is approximately Normal with µ = (nA)(nA+nB+1) 2 and variance σ 2 A = nAnB(nA+nB+1) 12 . Note that the variance is the
a. To determine if the two populations of crawfish from Devon and Cornwall have the same mean carapace length, we can use the two-sample t-test.
This test compares the means of two independent samples to assess whether they are significantly different.
We can calculate the sample means and sample standard deviations for both groups:
Next, we calculate the t-value using the formula:
To determine if this t-value is statistically significant, we need to compare it to the critical value from the t-distribution for the given degrees of freedom
If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that the two populations have different mean carapace lengths. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean carapace length between the two populations.
b. To answer the question using the Wilcoxon rank sum test, we need to combine the observations from both samples, assign ranks based on their relative positions, and calculate the sum of ranks for one of the samples (either Devon or Cornwall). The null hypothesis for this test is that the two distributions are the same.
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